Pascale Bréhonnet

Laguerre-Gram reduced-order modeling

We present an efficient model reduction procedure based on the Laguerre description of the system to be approximated. Using a one-order operator defined in the Laplace domain we construct a pencil of functions and formulate the problem as the minimization of the L/sub /spl infin///sup 2/(/spl Ropf//sup +/) criterion. The use of a weight function in the inner product definition allows a control of the time-error spreading in model reduction procedure. We show how the required Gram matrix can be computed efficiently and prove that the impulse response of the reduced model is also in L/sub /spl infin///sup 2/(/spl Ropf//sup +/). The transfer function approach allows an immediate and promising application in model reduction of infinite dimensional systems. An extension to multiple-input-multiple-output systems is also given.

A new discrete impulse response Gramian and its application to model reduction

Some fundamental properties of an impulse response Gramian for linear, time-invariant, asymptotically stable, discrete single-input-single-output (SISO) systems are derived. This Gramian is system invariant and can be found by solving a Lyapunov equation. The connection with standard controllability, observability, and cross Gramians is proven. The significance of these results in model-order reduction is highlighted with an efficient procedure.

Low Complexity Equivalent Circuit Models for VLSI Interconnects

In this paper we present a technique for generating low complexity equivalent circuit models for VLSI circuit interconnects via the Laguerre-Gram model order reduction (MOR) method developed by our team. We discuss model passivity and equivalent circuit implementation and then show the advantages of our method in preserving important signal parameters such as rise time, delay and overshoot

Gram matrix of a Laguerre model: application to model reduction of irrational transfer function

An efficient method for evaluating inner products of repeated integrals and derivatives of a function described by a Laguerre model is presented. An immediate and promising application is model reduction of infinite-dimensional transfer functions.

A frequency domain approach for efficient model reduction of mixed VLSI circuits

It has become well accepted that interconnect delay dominates gate delay in current VLSI circuits. This paper introduces a new method, based on a frequency domain approach, for the simulation of interconnect problems found in high speed digital circuits and SOC-AMS.

Fast communication: Efficient Gram-matrix computation for irrational resonant systems using Kautz models

We present a new method for evaluating the Gram matrix containing the inner products of repeated integrals and derivatives of irrational transfer functions via a Kautz model. The technique is particularly interesting for describing resonant systems and it has an immediate application in model order reduction.

An alternative method for numerical inversion of Laplace transforms

Based on least-squares approximation of the rectangular pulse (Vilbeacute , 1999) by exponential functions, this brief presents an alternative method for performing numerical inversion of the Laplace transform. It compares favourably with the celebrated Vlachs method

A numerical method for a full-wave electromagnetic analysis of systems on chip

In the context of RF and high-speed circuits, Systems On Chip with Analog and Mixed Signals (SOC-AMS), interconnect has becoming a dominant factor in determining circuit performance and reliability in deep submicron designs. Transmission line properties of on-chip wiring need to be taken into account due to the great lengths and fast rise times encountered. Coupling noise between adjacent interconnects can also cause catastrophic effects on the logical functionality and long-term reliability of a VLSI circuit. With these trends, the electrical phenomena that have to be investigated are governed by the electromagnetic theory. However, its impossible to proceed to a complete SOC - AMS analysis with a full wave electromagnetic numerical tool, due to the large scale integration. As interconnects are typically of very large size and high-order, model-order reduction becomes necessary for efficient SOC modeling, simulation, design and optimization. In this communication, a new method based on numerical inversion of Laplace transform and on a discrete model-reduction technique is presented for simulating peak crosstalk noise problems found in high speed digital circuits and SOC-AMS. The method, particularly efficient and easy to be implemented in a program, is useful for an electromagnetic simulation of a complete system.

Fast communication: Autocorrelation-invariant discrete-time functions and associated orthogonal sequences

The paper studies frequency domain characterization and properties of autocorrelation discrete-time functions. Such functions may be useful in the design and synthesis of signaling waveforms with prescribed autocorrelation functions.

Stable model order reduction method using Kautz functions: Application to VLSI circuits

In previous papers we presented MOR (model order reduction) methods based on the construction of a Gram matrix subsequent to a decomposition in Laguerre series. In this paper we propose an alternative solution using Kautz series, more adequate for modeling poorly damped systems.